Why are most research telescopes reflectors?

If you wanted to find something small in a dark basement, would you
use a magnifying glass or find a way to get more light?
Of course, you'd try to find more light. Astronomers do the same
thing -- the Universe is very big and the light coming from
other stars and galaxies is very dim.
For example, the nearest large galaxy to our own, Andromeda
(also called M31), is about six times the apparent diameter of the
Moon, but the Moon seems much larger than Andromeda even through
binoculars. Just enlarging the sky won't
solve the problem -- you don't just need a magnifying glass to find
something small in a dark basement. You need more light, so you need
to make a telescope that will collect a lot of light.
The bigger the diameter of the telescope you have, the more light you
can collect, and the better the images you can take. But, you also need to
have some way of focusing all the light you collect. Galileo's idea of
using glass lenses to focus the light from stars was thought to be the
best way to do this for some time.

BUT, one problem with glass lenses is that, like
prisms, they don't
bend light of all wavelengths evenly. Sometimes you want to break
up the light, but lenses will break up the light even when you don't
want it to. So,
even if you make a lens very carefully, when you take a picture of a
star with that single lens, you get a blob that is bluer on one edge
and redder on the other edge. This phenomenon is called chromatic
aberration. And there is nothing you can do about it!
...Well, almost nothing. You can minimize this effect if you
are clever about it -- the 40-inch actually has two 40-inch
lenses, made from two kinds of glass, crown and flint, which minimize
chromatic aberration. You can also use special filters to let in
only one color of light -- then all the light is aberrated
in the same way (since it's monochromatic). In the case of the
40-inch, we use greenish or yellow filters, and the first stellar photograph
through such a filter was taken in 1900.

Fortunately, mirrors reflect light of all (visible)
wavelengths in exactly the same way, so if you have a reflecting
telescope, you don't have to worry about chromatic aberration.

Another problem with lenses is that when they get very big they
get very heavy. And, because you don't want to block any star light,
you can only support a telescope lens around the
edge of the lens, which is also the thinnest, most fragile part of the
lens. You can't support the lens in any other way, otherwise you'll
block the light you're trying to collect.

Mirrors, on the other hand, don't have to be free and unsupported on
both sides because the light isn't going through them, it's
only bouncing off one side of them. So mirrors can be heavy
but you can support them well underneath and still not interfere with your
light collection.

The Yerkes 40-inch refractor is the largest refracting telescope in the
world; when it was completed (in 1897), it was the largest telescope in
the world of any sort. Today, the largest telescope in the world is a
reflector, the ten-meter, or 400-inch, Keck Telescope in
Mauna Kea,
Hawaii. The five-meter, or 200-inch, Hale Telescope at Palomar Mountain
in California is the largest reflector in the continental United
States. (For diameters of other large telescopes, see
Big
Eyes, a list of the world's largest optical telescopes.)

How much better are these telescopes at collecting light than the
40-inch? The light-collecting area of the telescope tube is proportional
to the diameter of the tube squared. Since the 40-inch is nearly one meter,
we can compare it to a 4-meter telescope like this:

so the 4-meter telescope is 16 times better at collecting light
than a 1-meter. The Keck can gather 10x10, or 100 times more light
than the Yerkes 40-inch refractor; the Hale Telescope can gather
5x5 = 25 times more light than the 40-inch. The University of
Chicago collaborates on the operation of another observatory called
Apache Point in New Mexico.
The main telescope there is a 3.5-meter, and so it collects 3.5x3.5 = 12.25
times more light than the 40-inch can. The telescopes that the
general public often buys are maybe 10 centimeters = 0.1 meters in
diameter. So, comparing the 40-inch to the 10-centimeter :

the 40-inch is 100 times better at gathering light than the 10-centimeter!
Clearly, light gathering power goes up fast as the size of your
telescope increases -- for a little increase in diameter, you get a lot
more light. In mathematical parlance, we say that it "goes as the square
of the diameter."

SO, in conclusion, astronomers prefer reflecting telescopes because they
can be made larger so that they collect more light, and because they don't have
chromatic aberration.

This then begs the question: So why did they make the Yerkes 40-inch
telescope a
refractor and not a reflector? At the time of the construction of
the 40-inch, no research-quality reflecting telescopes had ever been
made, so people who were doing serious research only worked with
refractors. At around the turn of the century, George W. Ritchey
(working here at Yerkes) was one of several people who
started to produce high-quality pictures from reflecting telescopes.
(He was working on a 24-inch telescope; although we have a 24-inch today, the
24-inch he worked on was replaced more than 30 years ago.)